Spray the 9x13 inch non-stick baking dish with a non-stick cooking spray.
Put the butter in a microwave-safe bowl and melt the butter in a microwave. Mix the cocoa powder with the butter. Whisk the eggs, sugar and vanilla in another large bowl. Add the butter and cocoa mixture to the egg and mix so everything is combined. Add flour, salt and baking powder to the liquid mixture, and stir until combined (don't overmix).
Pour the brownie batter into the baking dish, put in the oven on the middle rack and bake for 25 minutes. Make sure it's on the middle rack, not the top one (brownies on the top rack are too close to the heating element and turn out more cakelike).
When the brownie cools down, cut it into squares.
Notes
Do not overbake! Even if the brownie seems a little undercooked, it is fine - it will harden in a baking dish once it cools down. Resist the temptation to cook the brownie more - it will dry out if overcooked. As long as you FULLY pre-heated the oven before putting in the brownies and use the correct size (9x13 inch rectangle) pan, 25 minutes baking time is enough.